2-Segal sets and pseudomonoids in the bicategory of spans
Category Theory
2025-05-30 v1 Algebraic Topology
Abstract
In this survey article, we give an introduction to the notion of a 2-Segal set and prove that 2-Segal sets are equivalent to pseudomonoids in the bicategory of spans. The proof utilizes graphical techniques for 2-Segal sets and spans that should be useful in more general settings. There are procedures for obtaining an associative algebra from a 2-Segal set (satisfying finiteness conditions). We describe these procedures and give several examples of algebras arising from 2-Segal sets. Wherever possible, we avoid higher category theory so as to make the paper accessible to a wide audience.
Cite
@article{arxiv.2505.22832,
title = {2-Segal sets and pseudomonoids in the bicategory of spans},
author = {Sophia E Marx and Rajan Amit Mehta},
journal= {arXiv preprint arXiv:2505.22832},
year = {2025}
}